The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  0  X

generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+35x^6+105x^8+168x^10+280x^12+435x^14+2048x^15+435x^16+280x^18+168x^20+105x^22+35x^24+1x^30

The gray image is a linear code over GF(2) with n=30, k=12 and d=6.
This code was found by Heurico 1.16 in 1.77 seconds.